News for STNB2015

It is a pleasure to remark that on Thursday January 29 there will be the special

(60 ± ε) - BIRTHDAYS SESSION

dedicated to:

Núria Vila, Enric Nart, Teresa Crespo and Àngela Arenas

We kindly ask you to fill this registration form and follow instructions for the payment. A few number of grants are available from the organization for young researchers. Contact by e-mail if you want to apply.

Properes xerrades: dijous 11 desembre 2014

Dec. 4, 2014, 11:57 p.m.

Dijous, 11 de desembre, 2014

Facultat de Matemàtiques, Universitat de Barcelona, Aula IMUB

15:00 h Recursive towers and graphs

E. Hallouin (Inst. Mathématiques de Toulouse)

Abstract: I will give a connection between recursive towers of curves over finite fields and graph theory. Then I will focus on the computation of the genus sequence. Integral bases computation is of great importance for this crucial step.

15:45 h Enumerating Extensions of p-adic fields with given invariants

S. Pauli (UNC Greensboro)

Abstract: It is well known that p-adic fields have a finite number of extensions of a given degree. With Ore’s conditions and Krasner’s mass formula, we can find all of the possible discriminants for such an extension and how many extensions have each discriminant. An algorithm of Pauli and Roblot uses these to enumerate extensions of given degree and discriminant. We look at finding Eisenstein polynomials that generate all totally ramified extensions of a given degree, discriminant, and additional invariants related to the ramification polygon. As we can find all possibilities for these invariants, this, together with methods of Maurizio Monge, forms the core of a new algorithm for enumerating all extensions of given degree that is far faster than current methods and only requires computation in the base field and its residue class field.